%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG020-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:45 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.55s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 21 ( 21 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
fof(f18,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).
fof(f22,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
fof(f23,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
fof(f25,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f24]) ).
fof(f28,axiom,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X1)),additive_inverse(multiply(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference3) ).
fof(f30,negated_conjecture,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form2) ).
fof(f31,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))),
inference(definition_unfolding,[],[f30,f18,f18,f18]) ).
fof(f32,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f23,f25]) ).
fof(f99,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f109,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f217,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X2,X1)) = add(multiply(additive_inverse(X0),X2),multiply(X0,additive_inverse(X1))),
inference(superposition,[],[f12,f32]) ).
fof(f220,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),add(multiply(X0,X2),X3)) = add(multiply(X0,add(X1,X2)),X3),
inference(superposition,[],[f15,f12]) ).
fof(f223,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X2,X1)) = add(multiply(X0,additive_inverse(X2)),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f217,f32]) ).
fof(f233,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X2,X1)) = multiply(X0,add(additive_inverse(X2),additive_inverse(X1))),
inference(forward_demodulation,[],[f223,f12]) ).
fof(f242,plain,
! [X2,X0,X1] : multiply(X0,add(additive_inverse(X2),additive_inverse(X1))) = multiply(X0,additive_inverse(add(X2,X1))),
inference(forward_demodulation,[],[f233,f32]) ).
fof(f306,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X2),add(multiply(X1,X2),X3)) = add(multiply(add(X0,X1),X2),X3),
inference(superposition,[],[f15,f13]) ).
fof(f642,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X0,X1))),
inference(superposition,[],[f14,f28]) ).
fof(f643,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X2)),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f642,f25]) ).
fof(f668,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(multiply(X0,additive_inverse(X2)),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f643,f25]) ).
fof(f693,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = multiply(X0,add(additive_inverse(X2),additive_inverse(X1))),
inference(forward_demodulation,[],[f668,f12]) ).
fof(f717,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = multiply(X0,additive_inverse(add(X2,X1))),
inference(forward_demodulation,[],[f693,f242]) ).
fof(f738,plain,
! [X2,X0,X1] : multiply(X0,additive_inverse(add(X2,X1))) = multiply(X0,additive_inverse(add(X1,X2))),
inference(forward_demodulation,[],[f717,f32]) ).
fof(f1111,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,u),y),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(superposition,[],[f31,f99]) ).
fof(f1147,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,u),y),add(add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),additive_inverse(multiply(x,multiply(u,y))))),
inference(forward_demodulation,[],[f1111,f109]) ).
fof(f1177,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,u),y),add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))))),
inference(forward_demodulation,[],[f1147,f15]) ).
fof(f1190,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(add(multiply(x,u),multiply(x,v)),y),add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y))))),
inference(forward_demodulation,[],[f1177,f306]) ).
fof(f1196,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(add(multiply(x,u),multiply(x,v)),y),additive_inverse(multiply(x,multiply(v,y))))),
inference(forward_demodulation,[],[f1190,f109]) ).
fof(f1200,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),multiply(add(multiply(x,u),multiply(x,v)),y))),
inference(forward_demodulation,[],[f1196,f14]) ).
fof(f1202,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),multiply(multiply(x,add(u,v)),y))),
inference(forward_demodulation,[],[f1200,f12]) ).
fof(f1203,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(x,additive_inverse(multiply(v,y))),multiply(multiply(x,add(u,v)),y))),
inference(forward_demodulation,[],[f1202,f25]) ).
fof(f1204,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(x,additive_inverse(multiply(v,y))),add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(u,y))))),
inference(forward_demodulation,[],[f1203,f109]) ).
fof(f1205,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(x,additive_inverse(multiply(v,y))),add(additive_inverse(multiply(x,multiply(u,y))),multiply(multiply(x,add(u,v)),y))),
inference(forward_demodulation,[],[f1204,f14]) ).
fof(f1206,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(x,additive_inverse(multiply(v,y))),add(multiply(x,additive_inverse(multiply(u,y))),multiply(multiply(x,add(u,v)),y))),
inference(forward_demodulation,[],[f1205,f25]) ).
fof(f1207,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(x,add(additive_inverse(multiply(v,y)),additive_inverse(multiply(u,y)))),multiply(multiply(x,add(u,v)),y)),
inference(forward_demodulation,[],[f1206,f220]) ).
fof(f1208,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,add(additive_inverse(multiply(v,y)),additive_inverse(multiply(u,y))))),
inference(forward_demodulation,[],[f1207,f14]) ).
fof(f1209,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,additive_inverse(add(multiply(v,y),multiply(u,y))))),
inference(forward_demodulation,[],[f1208,f242]) ).
fof(f1210,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,additive_inverse(add(multiply(u,y),multiply(v,y))))),
inference(forward_demodulation,[],[f1209,f738]) ).
fof(f1211,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,additive_inverse(multiply(add(u,v),y)))),
inference(forward_demodulation,[],[f1210,f13]) ).
fof(f1212,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,multiply(add(u,v),additive_inverse(y)))),
inference(forward_demodulation,[],[f1211,f25]) ).
fof(f1213,plain,
add(multiply(multiply(x,add(u,v)),y),multiply(x,additive_inverse(multiply(add(u,v),y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,multiply(add(u,v),additive_inverse(y)))),
inference(forward_demodulation,[],[f1212,f25]) ).
fof(f1214,plain,
add(multiply(multiply(x,add(u,v)),y),multiply(x,multiply(add(u,v),additive_inverse(y)))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,multiply(add(u,v),additive_inverse(y)))),
inference(forward_demodulation,[],[f1213,f25]) ).
fof(f1215,plain,
$false,
inference(trivial_inequality_removal,[],[f1214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG020-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.40 % Computer : n015.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun Sep 27 23:02:31 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.46 Running first-order model finding
% 0.16/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.55 % (2113682)Will run a generic schedule for satisfiability detection.
% 0.23/0.55 % (2113693)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=688687436:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.55 % (2113687)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4146043978_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.55 % TRYING [1]
% 0.23/0.55 % TRYING [2]
% 0.23/0.55 % (2113688)% WARNING: option uhcvi not known.
% 0.23/0.55 % TRYING [3]
% 0.23/0.55 % (2113690)dis+10_1_sil=32000:sp=arity:random_seed=2829118745:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.55 % (2113691)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1694798524:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.55 % (2113692)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3410525623:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.55 % (2113689)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2588557572:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.55 % (2113688)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=702753071:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.55 % TRYING [4]
% 0.23/0.55 % (2113691) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2113682-2113691"...
% 0.23/0.55 % (2113691)...printing done.
% 0.23/0.55 % (2113691)Refutation found. Thanks to Tanya!
% 0.23/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.56 % (2113691)------------------------------
% 0.23/0.56 % (2113691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.56 % (2113691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.56 % (2113691)CaDiCaL version: 2.1.3
% 0.23/0.56 % (2113691)Termination reason: Refutation
% 0.23/0.56 % (2113691)Time elapsed: 0.040 s
% 0.23/0.56 % (2113691)Peak memory usage: 12 MB
% 0.23/0.56 % (2113691)Instructions burned: 39 (million)
% 0.23/0.56 % (2113682)Success in time 0.081 s
% 0.23/0.56 % Vampire exiting
%------------------------------------------------------------------------------